Question

Refer to the accompanying table, which desores results from groups of births from different sets of parents. The random represents the number of girls among 8 children Find the mean and standard deviation for the number of pirtis in i Click the icon to view the datatable The meanis (Round to one decimal place as needed.) The standard deviation is gir) (Round to one decimal place as needed)

Answer 1

bolun - X: is random voniable such thall it represents number 0% givis among 8 children. The pmf of x is Number of girls (x) P(x) 0 0.004 0.025 - 2 4 5 0.118 0.218 0.262 0.224 0:119 0.028 0.002 a 7 8 8. Mean: 4= E(X) = Ž x CPCX=00)) x=0 = 0*0.004 + 1* 0.025 + 2*0.118 + 3*0.218 + +4*0.262 + 5*0.224 + 6*0.119 + 7 +0.028 + 8 + 0.002 M = 4.009 =4.0 8 E(X²) = Ž x2* P(X=2) X=0 0²*0.004 + 1 2 - 120.025 + 2² x 0 118 + + 8 h * 0.002 -- E(x)= 18.035 .. Var (x) = E(X2) - [E(x)]? = 18.035 - (4.009)2 .. Var (x) - 1.962919 Standard deviation ſvar(x) = 51.962919 . Standard deviation = 1.40104 1.4 The mean is 4 = 4.009 girls = 4.0 girls The standard deviation is o= 1. 40104 girls = 1.4 girls